Question: The sum of two numbers is $58$, and their difference is $6$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 58}$ ${x-y = 6}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 64 $ $ x = \dfrac{64}{2} $ ${x = 32}$ Now that you know ${x = 32}$ , plug it back into $ {x+y = 58}$ to find $y$ ${(32)}{ + y = 58}$ ${y = 26}$ You can also plug ${x = 32}$ into $ {x-y = 6}$ and get the same answer for $y$ ${(32)}{ - y = 6}$ ${y = 26}$ Therefore, the larger number is $32$, and the smaller number is $26$.